Clarke-Wright Savings — An Interactive Vehicle Routing Simulator

What this simulation shows

The Vehicle Routing Problem is easy to state and brutally hard to solve exactly: given a depot, a set of drops, and vehicles with finite capacity, what is the cheapest set of routes that serves everyone? The number of possible answers grows faster than any computer can enumerate, so commercial systems do not look for the perfect answer. They look for a very good one, quickly.

Clarke and Wright published the classic way of doing that in 1964, and versions of it are still running inside transport optimisation software today. The idea is almost embarrassingly simple. Start from the worst sensible plan: send a separate vehicle out and back for every single drop. Then, for every pair of drops, work out how much distance you would save by serving them on one trip instead of two. Sort those savings from largest to smallest and work down the list, merging routes whenever capacity allows.

This simulator lets you watch that happen on a West Yorkshire map, one merge at a time, with the savings table visible beside it.

How to use it

Press Step merge repeatedly rather than jumping straight to Auto run. The first few merges are the interesting ones: they are the large, obvious consolidations that any experienced planner would spot immediately, and seeing the algorithm find them in the same order is what makes the heuristic feel reasonable rather than magical.

Then use the two controls to break it deliberately.

Drop Vehicle capacity and re-run. Merges that were previously top of the savings list become infeasible, so the algorithm skips them and takes the next best option. The resulting plan is worse, but not because the algorithm got worse — the constraint changed. This is the single most common source of “why did the routes change overnight?” questions in real operations.

Adjust Planning speed to slow the animation down and read the Earl explanation panel as each merge lands. It narrates why that particular pair was chosen at that particular moment.

What to take away

Two things are worth noticing. First, the algorithm is greedy: it takes the best available saving right now and never reconsiders. That makes it fast and explainable, and it also means the final plan is usually good but rarely optimal — which is the gap that Two-Opt, Simulated Annealing, and Tabu Search exist to close.

Second, the savings list is a ranking of pairs, not a plan. The plan is what emerges after capacity, time windows, and vehicle rules have filtered that ranking. When a planner says the system “made a stupid decision”, it is usually the filter rather than the ranking that did it.

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